1 Trim your artichokes (see How to Trim an Artichoke). Once they are trimmed, slice lengthwise into pieces roughly ¼ inch thick. You want them to look like silhouettes of an artichoke heart.
2 Bathe the slices in a bowl of lemon juice.
3 Get a large, heavy pot with a lid and pour in a layer of olive oil. Add the smashed garlic cloves and turn the heat to low.
4 Take some artichoke heart slices out of the lemon juice and salt them well. Slip them into the olive oil in layers, adding more olive oil to cover. You will probably need about a pint or so of olive oil – it is very important they are completely covered. Do not use cheap vegetable oil (corn, canola, etc) as a substitute because you will definitely taste the olive oil in the final dish. You could use melted butter, though…
5 Cover the pot and cook on the lowest heat of your weakest burner for 45 minutes. Turn off the heat and let the oil cool for another 20-30 minutes.
6 To make the salad, just remove the artichokes from the oil and toss with the remaining ingredients. You can eat the garlic or not, but it is just there to flavor the oil.
Serve at room temperature. It keeps for several days in the fridge.